A flying robot often encounters scenarios requiring it to fly through a window on a wall or a narrow orifice, while ensuring that it does not collide with the surrounding edges. This is particularly difficult when the relative sizes of the robot and the window/orifice are such that the window/orifice is just barely large enough for the robot to fly through. In such scenarios, the maneuver through the orifice needs to be one of high precision, and the shapes of the robot and the orifice play an important role.
The problem of an autonomous robot going through an orifice, although of great practical importance, has received somewhat limited attention in the literature. In one approach, the authors address the problem of flying a quadrotor through a window by defining a goal point in the window, treating that goal point as a terminal condition to be achieved by the quadrotor and then numerically integrating the dynamic equations of the quadrotor backward in time to determine a reference trajectory for the quadrotor in a high dimensional space. A controller that ensures that the quadrotor tracks this reference trajectory is then designed. With this approach, every time the goal point/window moves or is subjected to a disturbance, the differential equations governing the quadrotor dynamics have to be numerically integrated afresh to compute an updated reference trajectory. Another approach involves the formulation of an optimization problem that incorporates the physical dimensions of the opening as constraints and then determines optimal trajectories for the quadrotor through this opening. Experimental results of the quadrotor flying through a hoop are presented. As the window moves, the constraints change, and the optimization problem needs to be solved afresh. Researchers have also developed a Linear Quadratic Gaussian (LQG)-obstacle technique and used this technique to demonstrate simulations of a quadrotor flying through a window. A related problem is that of a snake robot going through an elevated passage in a wall. However, all these documents rely on numerically generating the robot trajectory through the passage. This is where the current document differs from the existing literature.